BAGHDAD — Defense Secretary Robert Gates said Monday he foresees a shrinking U.S. combat role in Iraq in coming months, while the No. 2 U.S. commander here cautioned that it would be a mistake to push the U.S.-trained Iraqi army and police into a leading security role too soon.

"I'm not sure that pushing them forward is the right thing that we want to do. We tried that once before and found that that didn't work," Lt. Gen. Lloyd Austin told reporters, referring to the pre-2007 U.S. strategy, which focused on handing off security responsibility to the Iraqis fast while reducing the U.S. presence. That approach faltered, leaving Iraq on the brink of all-out civil war before President Bush switched strategies and put Gen. David Petraeus in charge in Baghdad.

Austin said key measures of insurgent violence today are about 80 percent lower than one year ago.

Petraeus is scheduled to hand off on Tuesday to his successor, Lt. Gen. Ray Odierno. Odierno, who served for 15 months as the No. 2 U.S. commander here before leaving last February, will be promoted to four-star rank at a separate ceremony prior to the formal change-of-command ceremony.

Gates, who planned to preside at the change-of-command ceremony, told reporters traveling with him on an overnight flight from Washington that conditions have improved enough to permit a continuation of the process of handing off responsibility to the Iraqi security forces. Last week he told Congress that the war was now in the "endgame," with U.S. forces drawing back to a secondary role.

Bombings in Baghdad and northeast of the capital killed at least 32 people Monday, Iraqi officials said, the latest in an apparent bid by insurgents to chip away at growing public confidence in recent security gains.

At least 20 were killed and 30 were wounded in a suicide bombing in an evening attack in Balad Ruz, 45 miles northeast of Baghdad, said Maj. Gen. Abdul-Karim al-Rubaie, the military commander of operations in Diyala province. Many of the dead were police.

A police officer said the attacker was a woman.

Although no additional U.S. combat brigades are to withdraw from Iraq this year, under a plan announced by Bush last week, Gates told reporters that he expects the U.S. combat role to keep shrinking. Pentagon commanders say they need more forces in Afghanistan, where fighting has worsened.

"We are clearly in a mission transition," he said.

On Monday, the Pentagon formally announced that a Marine Air-Ground task force, including the 3rd Battalion, 8th Marine Regiment, will go to Afghanistan in November to replace the two Marine units there now. The battalion is based at Camp Lejeune, N.C., and will be supplemented with aviation, headquarters and logistics units from across the Marine Corps.